Simple integration problem help

[Natasha1]

Could anyone explain to me ultra simply by means of a mechanical approach maybe why the integration of 1/(3-0.2x)dx = -5 ln l 3-0.2x l ? thanks

 

[quasar987]

set y = 3-0.2x

 

[Natasha1]

set y = 3-0.2x

What I don't get is the -5 before the ln l 3-0.2x l ?? :-(

 

[quasar987]

After you've set y = 3-0.2x, you also have to find dy in terms of dx. Do the calculations and you'll see where the -5 pops in.

 

[Natasha1]

After you've set y = 3-0.2x, you also have to find dy in terms of dx. Do the calculations and you'll see where the -5 pops in.

dy = -0.2 and then ?

 

[xman]

dy = -0.2 and then ?

right so
$$-\frac{1}{0.2} dy =dx\Rightarrow -\frac{1}{2/10} dy = dx \Rightarrow - \frac{10}{2} dy =dx \Rightarrow -5dy=dx$$

now substitute back into equation and integrate

 

[Natasha1]

right so
$$-\frac{1}{0.2} dy =dx\Rightarrow -\frac{1}{2/10} dy = dx \Rightarrow - \frac{10}{2} dy =dx \Rightarrow -5dy=dx$$

now substitute back into equation and integrate

thanks